JEE Mains · Chemistry · STD 11 - 5. Thermodynamics and thermochemistry

Given below are two statements:

Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.

Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below

A Both Statement I and Statement II are true
B Both Statement I and Statement II are false
C Statement I is true but Statement II is false
D Statement I is false but Statement II is true

Verified Solution

Answer & Solution

Correct Answer

(D) Statement I is false but Statement II is true

Step-by-step Solution

Detailed explanation

For an ideal gas, the relationship between heat capacity at constant pressure (\(C_p\)) and heat capacity at constant volume (\(C_v\)) is given by Mayer's relation: \(C_p - C_v = R\) Since the universal gas constant \(R\) is a positive value, \(C_p > C_v\). Thus, Statement I is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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